There is probably a very simple and obvious answer to this question, but right now it's just not clicking for me. So, perhaps someone else can help me out. Context: The typical undergrad intro to the Aharonov–Bohm effect is that it is an intrinsically non-classical phenomenon because an electron is effected by travelling through a region where E=0 and B=0. The claim is that, classically, regions with A≠0 but B=E=0 cannot have any effect on particles. Hence the 'quantumness' of the Aharonov–Bohm effect. So then, what about a toroidal transformer? (i.e. a toroidal loop of iron with a powered wire coil on one side and an unpowered wire coil on the other) We know that even if the coils don't touch the iron torus that the powered one can still induce a current in the unpowered one. However, unless I'm mistaken, you can construct such a device for which B=0 outside the iron. Yet the transformer still operates. Even more generally, Faraday's law says that an EMF will be induced in a loop of wire that encloses a changing magnetic field. As far as I know, it doesn't say anything about the B field having to be nonzero in the region where the wire loop is. One could imagine creating a confined changing B field, whether by using a superconducting shell or by using a Aharonov–Bohm type field configuration, and then surrounding it with a wire coil (that is, so that the coil is outside of the confinement region). Faraday's law would imply that an EMF will be induced in the wire, no? The question: Considering these two similar classical situations, how can one say that regions of A≠0 but B=E=0 produce no classical effect? It seems to me that electrons are affected by such regions in the case of classical induction.